Manifestation of the important role of nuclear forces in the emission of photons in pion scattering off nuclei

The bremsstrahlung of photons emitted during the scattering of ${\pi }^{+}$ mesons off nuclei is studied for the first time. The role of interactions between ${\pi }^{+}$ mesons and nuclei in the formation of the bremsstrahlung emission is analyzed in detail. We discover an essential contribution of photons emitted from nuclear part of the Johnson–Satchler potential to the full spectrum, in contrast with the optical Woods–Saxon potential. We observe an unusual essential influence of the nuclear part of both potentials on the spectrum at high photon energies. This phenomenon opens a new experimental way to study and check non-Coulomb and nuclear interactions between pions and nuclei via measurements of the emitted photons. We provide predictions of the bremsstrahlung spectra for pion scattering off ${}^{44}\mathrm{Ca}$.

Figure 1

Diagrammatic representation of the emission of the bremsstrahlung photons during the scattering of the ${\pi }^{+}$ meson off the ${}^{44}\mathrm{Ca}$ nucleus. Dashed and solid lines refer to pions and nucleons, respectively. Wavy lines indicate the outgoing bremsstrahlung photons.

Figure 2

The bremsstrahlung cross sections of photons emitted during the scattering of the ${\pi }^{+}$ mesons off the ${}^{44}\mathrm{Ca}$ nucleus at the bombarding energy of 116 MeV [parameters of calculations: the potential $V_N^{\left(WS\right)}$ and $V_N^{\left(JS\right)}$ are defined in Eqs. (3) and (2), parameters of these potentials are taken from Ref. [18] and Table 1 in Ref. [22], the angle ${\theta }_{\gamma }$ between directions of the photon emission and the $\pi$-meson motion is ${90}^{\circ }$]. (a) The bremsstrahlung spectra, where interactions between ${\pi }^{\pm }$ mesons and nuclei are described by the Woods–Saxon optical model. We show changes of the spectrum as a function of strength $U$ of the nuclear potential (3). One can see the stability of the calculations. (b) The bremsstrahlung spectra, where interactions between ${\pi }^{\pm }$ mesons and nuclei are defined in the Johnson–Satchler formalism (see blue solid line) and the Woods–Saxon optical model formalism (see red dashed line). One can see principally different behavior between the spectra. This difference is because two theories used in the basis of calculations of these bremsstrahlung spectra are essentially different (the Coulomb interactions and centrifugal potential terms are the same): the Johnson–Satchler formalism is based on the relativistic Klein–Gordon equation, while the optical model formalism is based on the nonrelativistic Schrödinger equation. Note that both spectra obtained by the Johnson–Satchler formalism and the optical model formalism with the Woods–Saxon potential coincide at low photon energies, which confirms our formalism and calculations (calculations are not normalized on any data point).

Figure 3

The bremsstrahlung cross sections of the emitted photons during the scattering of (a) $p+{}^{208}\mathrm{Pb}$ at the proton bombarding energy $E_{\mathrm{p}}=140$ MeV and (b) $p+{}^{197}\mathrm{Au}$ at the proton bombarding energy $E_{\mathrm{p}}=190$ MeV in comparison with experimental data (Edington, 1966 [43]) and (Goethem, 2002 [44]) (circular points) The calculations follow the formalism (Maydanyuk 2012 [30]) with electric component $p_{\mathrm{el}}$ defined in Eqs. (36) in that paper, without magnetic terms $p_{\mathrm{mag},1}$ and $p_{\mathrm{mag},2}$ in Eqs. (36) in Ref. [30], and without incoherent bremsstrahlung studied in Ref. [31]. The parameters of the proton-nucleus potential are taken from Eqs. (46) and (47) in (Maydanyuk, 2015 [31]) with the approximation $r_c=r_R=0.95$ fm. One can see the change of the spectra in the high-energy region as a function of nuclear strength $V_R$ of the proton-nucleus potential.